Question

An object with a mass of `5 kg` is pushed along a linear path with a kinetic friction coefficient of `u_k(x)= xe^x-x`. How much work would it take to move the object over #x in [1, 4], where x is in meters?

Answer 1

`W=147,15(3e^x-7)J`

Explanation:

`W=F_f*x=N int_1^4(x e^x-x) x*d x`
`W=m g int_1^4 (x^2 e^x-x^2)d x`
`W=m g ([e^x(x^2-2 x+2)]_1^4 - [1/3 x^3]_1^4)`
`W=m g(9e^x-21)`
`W=5*9,81(9e^x-21`
`W=147,15(3e^x-7)J`